To satisfy the high power demand, the multi-phase buck converter is used to replace the single-phase one. The benefits brought by the multi-phase buck converter are the high power density, quick transient response and cost efficient for high current solution. However, with different operating phase number, the profile of power efficiency is different. For light load operation, low operating phase number is preferred to increase the power efficiency by eliminating the switching loss. Thus, the down-phase mechanism, so-called “phase-shedding” technique, is used when the loading current becomes lower. Take a four-phase buck converter for example, as shown in FIG. 1, four phase circuits 10 are provided to convert an input voltage Vi to an output voltage Vo, an error amplifier 18 is connected to the output Vo of the multi-phase buck converter to detect the output voltage Vo to generate an error signal EA, an analog-to-digital converter (ADC) 16 is connected to the error amplifier 18 to convert the analog error signal EA into a digital error signal e[n], a digital compensator 14 is connected to the ADC 16 to compensate the digital error signal e[n] to generate a digital error signal e′ [n], and according to the compensated digital error signal e′[n], a digital pulse width modulation (DPWM) circuit 12 connected to the digital compensator 14 provides PWM signals PWM1, PWM2, PWM3 and PWM4 to drive the phase circuits 10 respectively. The DPWM circuit 12 may determine the operating phase number, i.e., how many of the phase circuits 10 to be operated with, according to the loading current Io, and then assert one or more of enable signals EN1, EN2, EN3 and EN4 to enable the corresponding phase circuits 10. Therefore, a four-phase buck converter with a phase shedding mechanism could change the operating phase number from one to four depending on the loading to optimize its power efficiency. FIG. 2 is a diagram showing the profile of power efficiency (η) of a four-phase buck converter when operating with different number of phase circuits, in which curves 20, 22, 24 and 26 represent the power efficiency at different loading (Io) in four-phase operation, three-phase operation, two-phase operation and single-phase operation respectively. As can be seen in FIG. 2, when the operating phase number is smaller, the buck converter has better power efficiency at lower loading; on the contrary, when the operating phase number is larger, the buck converter has better power efficiency at higher loading. The DPWM circuit 12 enables more phase circuits 10 for higher loading and enables fewer phase circuits 10 for lower loading. Thus, the phase shedding mechanism of a multi-phase buck converter can improve the power efficiency of the buck converter as the loading becomes low.
However, as the operating phase number changes, the control-to-output voltage transfer function of a multi-phase buck converter also changes. For example, if a multi-phase buck converter has a resonant frequency fc when operating with single phase circuit, the resonant frequency may become 1.414 fc and 2 fc when operating with two phase circuits and fourth phase circuits respectively. In the conventional designs, a multi-phase buck converter has a single digital compensator, such as the one shown in FIG. 1, so the digital compensator is designed based on a single-phase or four-phase control-to-output voltage transfer function.
With a loop gain bandwidth (BW) of 40 KHz and a phase margin (PM) about 60° as the design target, FIG. 3 shows the frequency response of the multi-phase buck converter of FIG. 1 when the digital compensator 14 is a single-phase based design, in which curves 30 and 32 represent the frequency response obtained in single-phase operation, curves 34 and 36 represent the frequency response obtained in two-phase operation, and curves 38 and 40 represent the frequency response obtained in four-phase operation. FIG. 4 shows the phase margin and bandwidth of the multi-phase buck converter in single-phase, two-phase and four-phase operations, respectively, when the digital compensator 14 is a single-phase based design. FIG. 5 shows the frequency response of the same multi-phase buck converter when the digital compensator 14 is a four-phase based design, in which curves 42 and 44 represent the frequency response obtained in single-phase operation, curves 46 and 48 represent the frequency response obtained in two-phase operation, and curves 50 and 52 represent the frequency response obtained in four-phase operation. FIG. 6 shows the phase margin and bandwidth of the multi-phase buck converter in single-phase, two-phase and four-phase operations, respectively, when the digital compensator 14 is a four-phase based design. Referring to FIGS. 3 to 6, if the digital compensator 14 is designed based on a single-phase control-to-output voltage transfer function, there will be insufficient phase margin when the buck converter operates with four phase circuits. On the other hand, if the digital compensator 14 is designed based on a four-phase control-to-output voltage transfer function, the bandwidths for single-phase and two-phase operations reduce, leading to degraded transient response in single-phase operation and in two-phase operation.
Therefore, it is desired a multi-phase buck converter with operating phase number dependent compensation.